What are some 3rd party rendering engines available for Blender?
A few open source engines which come to mind immediately:


Luxrender
Yafaray
TheBounty, a fork of YafaRay
POV-Ray (exporter)
Aqsis
Jot (exporter)
Mitsuba implement biased and unbiased rendering techniques (Exporter)


Some non-open source engines:


Octane, fast GPU renderer integrated into blender (Commercial)
Vray, production proven render engine. (Commercial)




Also see the answer on the resources post for even more.